Cat Factor Analysis

7/30/2019 Cat Factor Analysis

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Factor Analysis

1. Problem Formulation: mcari yg mdasari hubungan antara perilaku rumah tangga dan perilaku

belanja.

Tujuannya apa? To understand the relationship between household behavior and shopping

behavior.

Samples size = 25 respondents. Variables: use 7 variables of lifestyle statements on a seven-point scale (1=strongly disagree;

7=strongly agree).

1. V1= I would rather spend a quiet evening at home than go out to a party.

2. V2=I always check prices, even on small items.

3. V3= Magazines are more interesting than movies.

4. V4=I will not buy product advertised on bill boards.

5. V5= I am a homebody.

6. V6= I save and cash coupons.

7. V7= Companies waste a lot of money advertising.

2. Construct correlation matrix: dicari yg diatas 0.5

Correlation Matrixa

V1 V2 V3 V4 V5 V6 V7

Correlation V1 1.000 -.004 .628 .082 .675 -.100 -.338

V2 -.004 1.000 .151 -.248 .048 .582 -.251

V3 .628 .151 1.000 -.182 .480 .090 -.588

V4 .082 -.248 -.182 1.000 .272 .017 .469

V5 .675 .048 .480 .272 1.000 -.110 -.082

V6 -.100 .582 .090 .017 -.110 1.000 .014

V7 -.338 -.251 -.588 .469 -.082 .014 1.000

Sig. (1-tailed) V1 .493 .000 .348 .000 .316 .049

V2 .493 .236 .116 .409 .001 .113

V3 .000 .236 .192 .008 .334 .001

V4 .348 .116 .192 .094 .469 .009

V5 .000 .409 .008 .094 .301 .348

V6 .316 .001 .334 .469 .301 .473

V7 .049 .113 .001 .009 .348 .473

a. Determinant = .062

See correlation matrix: Some correlation coefficient are moderate (sekitar 0.5 sampai 0.75) andsignificant. Di atas 0.75 itu tinggi. Pokoknya dicari yg >0.5 dan yg signifikan.

Barlett test: Ho= The variables are uncorrelated in population. The p-value of Barletts test= 0.000,

so Ho is rejected. The variables are correlated; therefore analysis factor can be conducted or is

appropriate.

KMO= 0.55>0.50, factor analysis is appropriate.


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KMO and Bartlett's Test

Kaiser-Meyer-Olkin Measure of SamplingAdequacy.

.550

Bartlett's Test ofSphericity

Approx. Chi-Square 57.994

df 21Sig. .000

3. Determine the Method of Factor Analysis:

Use principal components analysis

4. Determine the Number of Factors:

Factor analysis ada 2:

Explanatory FAthe researcher does not determine number of factors. Factor analysis will do it.

Confirmatory FA the researcher determine number of factors before factor analysis is done.

Ways to determine number of factors:

1. A priory determination: Extraction number of factors. Misal kita isi 2, tar factornya jadi

2, dst.Component Matrixa

Component

1 2

V1 .817 .378

V2 .279 -.714

V3 .887 -.027

V4 -.204 .634

V5 .664 .505

V6 .050 -.604V7 -.684 .383

Extraction Method:Principal ComponentAnalysis.

a. 2 components extracted.

2. Determination Based on Eigenvalues: Ini ditentukan oleh SPSS nya dgn klik eigen value

nya. Eigen value kriterianya >1.

3. Determination Based on Scree Plot:

Dgn melihat kurva itu patahnya dimana dlm kasus ini 4. Klo pake scree plot biasanya >1

(lbh byk 1 faktor hasil penentuannya daripada pakai eigen value). Kelemahannya ga pasti utksituasi tertentu.


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4. Determination Based on Percentage of Variance: ada pengekstrakan di 7 variabel mjd

lebih kecil. 60%.

5. Determination Based on Split-HalfnReliabilty: dibelah 2.

6. Determination Based onSignificance Test: Kelemahannya sampelnya harus relative besar.

Kalau pakai Eigenvalues maka Factornya yg >1 ada 3.

Kalau pakai percentage of factor maka ada 3. Dilihat kumulatif akhirnya, itu total 80% jadi

ada 3, bisa juga Cuma 1 tapi pasti lebih dari 60% biasanya. 33+24=57, dst.

Biasanya Eigenvalues dan percentage selaras.

Total Variance Explained

Component

Initial EigenvaluesExtraction Sums of Squared

LoadingsRotation Sums of Squared

Loadings

Total % of VarianceCumulative

% Total% of

VarianceCumulative % Total

% ofVarianc

e Cumulative %

1 2.485 35.505 35.505 2.485 35.505 35.505 2.315 33.076 33.076

2 1.821 26.013 61.518 1.821 26.013 61.518 1.731 24.729 57.805

3 1.339 19.131 80.649 1.339 19.131 80.649 1.599 22.844 80.649

4 .508 7.258 87.907

5 .376 5.373 93.2806 .279 3.990 97.270

7 .191 2.730 100.000

Extraction Method: Principal ComponentAnalysis.

5. Rotate Factors: Matriks factor yg dirotasi.

Method of rotation: Varimax.

Factor loadings are simple correlations between the variables and the factors .

Factor Loading:

1. V1 (.897), V3 (.762), V5 (.868) have high correlation with factor 1.

2. V4 (.867) and V7 (.817) have high correlation with factor 2.3. V2 (.860) and V6 (.911) have high correlation with factor 3.


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Rotated Component Matrixa

Component

1 2 3

V1 .897 -.082 -.076V2 .049 -.232 .860

V3 .762 -.440 .125

V4 .214 .867 -.052

V5 .868 .224 -.017

V6 -.057 .091 .911

V7 -.351 .817 -.073

Extraction Method: PrincipalComponent Analysis.Rotation Method: Varimax with

Kaiser Normalization.a. Rotation converged in 4 iterations.

Kesimpulannya dari 7 variabel mjd 3 faktor!

6. Determination based on significance:

A factor can then be interpreted in terms of the variables that load high on it.

Factor 1 consist of V1,V3 and V5:

V1= I would rather spend a quiet evening at home than go out to a party.

V3= Magazines are more interesting than movies.

V5= I am a homebody.

The underlying dimension of factor 1 is the existence at home.

Factor 2 consist of V4 and V7:

V4= I will not buy product advertised on bill boards.

V7= Companies waste a lot of money advertising.

The underlying dimension of factor 2 is attitude to advertisement.

Factor 3 consist of V2 and V6:

Factor loading


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V2= I always check prices, even on small items.

V6= I save and cash coupons.

The underlying dimension of factor 3 is carefulness in shopping.

7. Calculate factor scores:

Scoressave as variables.

Component Matrixa

Component

1 2 3

V1 .817 .378 .087

V2 .279 -.714 .457

V3 .887 -.027 -.043

V4 -.204 .634 .597

V5 .664 .505 .329

V6 .050 -.604 .689

V7 -.684 .383 .426

Extraction Method: PrincipalComponent Analysis.

a. 3 components extracted.

The factor scores for the ith factor may be estimated as follows:

Equation of factor1 F1= 0.817V1+0.279V2+0.887V3-0.204V4+0.664V5+0.050V6-0.684V7

Utk Factor 2 dan 3 buat sdri. Intinya klo tar dimasukkan tiap V1 V7ke dalam rumus akan ketemu

factor scoresnya

8. Select Surrogate Variables:See: Rotated component Matrix Table.

Rotated Component Matrixa

Component

1 2 3

V1 .897 -.082 -.076

V2 .049 -.232 .860

V3 .762 -.440 .125

V4 .214 .867 -.052

V5 .868 .224 -.017V6 -.057 .091 .911

V7 -.351 .817 -.073

Extraction Method: PrincipalComponent Analysis.Rotation Method: Varimax with

Kaiser Normalization.

a. Rotation converged in 4 iterations.

Use the highest loading for each factor.

Factor 1 is surrogated by V1 (0.897).



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9. Determine the Model Fit:

See reproduced correlation table-residual Part:

Residuals are the differences between the observed correlations and the reproduced

correlations can be examined by determine model fit. The smaller residuals, the fitter themodel is.

We that there are only 3 residuals that have values higher than 0.1. Therefore, it can be

concluded that the factor models are appropriate with data or the model are acceptable.

Reproduced Correlations

V1 V2 V3 V4 V5 V6 V7

ReproducedCorrelation

V1 .818a -.002 .711 .125 .762 -.127 -.377

V2 -.002 .796a .247 -.236 -.025 .760 -.269

V3 .711 .247 .790a -.224 .561 .031 -.636

V4 .125 -.236 -.224 .800a .381 .019 .637

V5 .762 -.025 .561 .381 .805a -.045 -.121

V6 -.127 .760 .031 .019 -.045 .841a .028

V7 -.377 -.269 -.636 .637 -.121 .028 .796a

Residualb V1 -.001 -.083 -.043 -.087 .027 .040

V2 -.001 -.096 -.012 .073 -.177 .018

V3 -.083 -.096 .042 -.081 .060 .048

V4 -.043 -.012 .042 -.110 -.002 -.167

V5 -.087 .073 -.081 -.110 -.065 .038V6 .027 -.177 .060 -.002 -.065 -.013

V7 .040 .018 .048 -.167 .038 -.013

Extraction Method: Principal Component Analysis.

a. Reproduced communalities

b. Residuals are computed between observed and reproduced correlations. There are 10 (47.0%)nonredundant residuals with absolute values greater than 0.05.

SEM 2 models of test:

- Structural theory model and test relationship among latent variables (contoh:

kepercayaan/trust).- Measurement theory model and testrelationship between latent variable and observed

variable or indicators.

- Endogenvariabel yg dipengaruhi oleh variable lain.

- Eksogentidak dipengaruhi variabel lain tp mempengaruhi variabel lain.

Konsturkvariable tp di alam abstrak (konsep).


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Cat Factor Analysis